Year: 2012
Type: preprint
Abstract: We prove that the outer Lipschitz geometry of a germ $(X,0)$ of a normal complex surface singularity determines a large amount of its analytic structure. In particular, it follows that any analytic family of normal surface singularities with constant Lipschitz geometry is Zariski equisingular. We also prove a strong converse for families of normal complex hypersurface singularities in $\mathbb C^3$: Zariski equisingularity implies Lipschitz triviality. So for such a family Lipschitz triviality, constant Lipschitz geometry and Zariski equisingularity are equivalent to each other.
Source: arXiv (Cornell University)
Authors: Neumann, Walter D., Pichon, Anne
Institutions: Columbia University, Institut de Mathématiques de Marseille
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1557025587